Yukawa-Tsuno plot

The Yukawa-Tsuno equation continues to find considerable application. 1-Arylethyl bromides react with pyridine in acetonitrile by unimolecular and bimolecular processes.These processes are distinct there is no intermediate mechanism. The SnI rate constants, k, for meta or j ara-substituted 1-arylethyl bromides conform well to the Yukawa-Tsuno equation, with p = — 5.0 and r = 1.15, but the correlation analysis of the 5 n2 rate constants k2 is more complicated. This is attributed to a change in the balance between bond formation and cleavage in the 5 n2 transition state as the substituent is varied. The rate constants of solvolysis in 1 1 (v/v) aqueous ethanol of a-t-butyl-a-neopentylbenzyl and a-t-butyl-a-isopropylbenzyl p-nitrobenzoates at 75 °C follow the Yukawa-Tsuno equation well, with p = —3.37, r = 0.78 and p = —3.09, r — 0.68, respectively. The considerable reduction in r from the value of 1.00 in the defining system for the scale is ascribed to steric inhibition of coplanarity in the transition state. Rates of solvolysis (80% aqueous ethanol, 25 °C) have been measured for 1-(substituted phenyl)-l-phenyl-2,2,2-trifluoroethyl and l,l-bis(substi-tuted phenyl)-2,2,2-trifluoroethyl tosylates. The former substrate shows a bilinear Yukawa-Tsuno plot the latter shows excellent conformity to the Yukawa-Tsuno equation over the whole range of substituents, with p =—8.3/2 and r— 1.19. Substituent effects on solvolysis of 2-aryl-2-(trifluoromethyl)ethyl m-nitrobenzene-sulfonates in acetic acid or in 80% aqueous TFE have been analyzed by the Yukawa-Tsuno equation to give p =—3.12, r = 0.77 (130 °C) and p = —4.22, r — 0.63 (100 °C), respectively. The r values are considered to indicate an enhanced resonance effect, compared with the standard aryl-assisted solvolysis, and this is attributed to the destabilization of the transition state by the electron-withdrawing CF3 group. 

The Br0nsted-type plot of the reaction between a series of 18 Y-phenyl benzoates (6) (Scheme 3) with CN in H2O/DMSO (4 1) at 298 K was linear with jSjg = -0.49. A Yukawa-Tsuno plot was also linear with Py = 137 and r=0.34 and these data pointed to a concerted mechanism in the formation of benzoyl cyanide (8). ... 

The reaction of a series of anilines with methyl 2,4,6-trinitrophenyl carbonate in water proceeded via a concerted mechanism as revealed by a linear Br0nsted-type plot with slope of 0.7. A Yukawa-Tsuno plot was linear for the alkaline hydrolysis of a series of Y-phenyl phenyl carbonates with p = 1.21 and r = 0.33, consistent with a concerted mechanism. 

The kinetics of the aminolysis of 5 -4-nitrophenyl X-thiobenzoates (39) by a series of alicyclic secondary amines in H2O/DMSO (4 1) at 298 K were determined and yielded excellent linear Yukawa—Tsuno plots for piperidine, piperazine, and morpholine with p = 0.90-1.23 and r=0.57-0.67. It was thus concluded that the mechanism of the aminolysis of (39) is stepwise, with breakdown of the tetrahedral intermediate being rate determining." ... 

A Yukawa-Tsuno plot was also linear with p = 0.95 and r=0.55, the magnitude of the r value implying that a negative charge develops partially on the O atom of the leaving group, from which it was concluded that the reaction proceeded through a concerted mechanism." ... 

Analyses of the kinetic data through LEER (i.e., Brpnsted-type, Hammett and Yukawa-Tsuno plots) showed that the mechanism of the reaction between aryl are-nesulfonates ArS020Ar and potassium ethoxide EtOK was concerted. As ion-paired EtOK was more reactive than the dissociated EtO , catalysis by the K" " ion was indicated, and it was proposed that K+ does so by increasing the electrophilicity of the... 

The Yukawa-Tsuno r values have been measured for the solvolysis reactions fonning benzyl cations and several a-substituted derivatives, 6-3IG charges and bond orders have been calculated for the presumed cationic intermediates. Analyze the data for relationships between r and the structural parameters. (Hint. Plot r versus the bond orders and the charges at C-1, C-2, C-3, and C-4.)... 

As the data in Table 1 indicate, there is a strong dependence of the hydration on the electron demands of the substituents, with a rho of -4.3 in the Yukawa-Tsuno (18) equation, where logk is plotted against p[a + t a — a)]. Partial hydration of CsHsC CT and recovery of the unreacted starting material did not result in any loss of specific activity, which indicates that the protonation of the triple bond is not significantly reversible and hence is rate determining. 

Upward curvature has been observed in the pa plots for stilbene, styrene and a-methylstilbene bromination in methanol (Ruasse and Dubois, 1972 Ruasse et al, 1978 Ruasse and Argile, 1983). In no case can these curvatures be interpreted coherently by Yukawa-Tsuno equations in terms of variable contributions of polar and resonance effects. Application of the multipathway scheme (Ruasse, 1990) leads to the results summarized in Table 4. 

Relative activation enthalpies (Aif) in Table 2 were converted to o% kx k ) at 298 K, and were plotted against Hammett a constants. Here, we used enthalpies, because the size of the entropy and hence the free energy depend much on low frequencies, which are less reliable than higher frequencies, especially for compounds with weak interactions such as TS (8). The use of free energy (AG ) gave similar correlations with more scattered points. As for the Hammett o constant, we used dual-parameter o constants in the form of the Yukawa-Tsuno equation (LArSR equation) (9) as defined in eq 3. Here, the apparent a constant (aapp) has a variable resonance contribution parameter (r), which varies depending on the nature of the reaction examined for t-cumyl... 

The solvolysis rates of 2-(dimethylphenylsilyl)-l-(Y-phenyl)ethyl 3,5-dinitroben-zoates (62) in 60% aqueous ethanol were analysed using using the Yukawa-Tsuno equation.103 The p value of -2.95 with r 1.04 found by changing the a-aryl substituent was much smaller than the p value of -5.45 found for the corresponding non-silylated system. This, the fact that the rate constant for the silylated substrate was > 105-fold faster than the rate of the non-silylated compound, and the small a value of 0.52 found from the log( Y/ H)si = a log( Y/ H)non-si plot was taken as evidence that the reaction of the silyl compound occurred via a tight transition state with significant neighbouring silyl participation (Scheme 25). 

Substituent effects on the hydrolysis rate of diethyl benzal in 50 % dioxane—water at 30 °C follow the Hammett relationship with p = —3.35 if log (k/kQ) is plotted versus the sigma values of meta substituents [163]. Data for electron-releasing para substituents exhibit positive deviations. The deviations are negative, however, if the data are plotted versus a + rather than a. A good linear relationship is obtained by application of the Yukawa—Tsuno equation [185]... 

Fujio and co-workers studied the reaction of pyridine with a wide range of 1-arylethyl bromides in acetonitrile. By careful analysis of the kinetic data, they were able to dissect each reaction into a first-order and a second-order component, as shown in the table below. The first-order components were correlated by a Yukawa-Tsuno equation logk/k = 5.0(a° + 1.15ct+). The second-order component gave a curved plot, as shown in Figure 4.P18. Analyze the responses of the reaction to the aryl substituents in terms of transition state structures. 

Fig. 29. Decomposition of acetophenone-bisulphite complexes [105c]. Inequality of inductive and resonance interactions causes a U-shaped free energy correlation in the simple Hammett approach. Yukawa-Tsuno type correction of the mesomerically donating groups is illustrated by the horizontal lines leading to a linear plot.

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